Question

A potentiometer wire of $4\text{m}$ long having resistance $12\Omega$ is connected in series with a resistance of $1988\Omega$ and a cell of emf $2\text{V}$. What is the potential gradient along the wire ?

• A. $0.002\text{V/m}$
• B. $0.004\text{V/m}$
• C. $0.001\text{V/m}$
• D. $0.003\text{V/m}$

Answer 1

The correct option is D $0.003\text{V/m}$

Given:
$R_{PQ}=12\Omega ;R=1988\Omega ;E=2\text{V}$

Current in the circuit,
$i=\frac{E}{R+R_{PQ}}=\frac{2}{1988+12}=\frac{1}{1000}\text{A}$

Voltage drop across points $\text{PQ}$ will be

$V_{PQ}=i\times R=\frac{1}{1000}\times 12=\frac{12}{1000}\text{V}$

So, the potential gradient across the wire will be

$\frac{V_{PQ}}{l}=\frac{\frac{12}{1000}}{4}=0.003\text{V/m}$

Hence, option $\left(D\right)$ is correct.